Today, most civil aircraft are equipped with a flight management system, commonly abbreviated FMS. An FMS consists of various functional components which allow notably the crew of the aircraft to define a flight plan on the basis of departure and arrival points and of a navigation database. A flight plan furthermore comprises a chronological sequence of waypoints described by their three-dimensional position and optionally their scheduled flyby time. On the basis of the flight plan, of the navigation database and of a database of performance of the aircraft, the FMS can determine a three-dimensional trajectory and a speed profile to be followed by the aircraft. The three-dimensional trajectory is formed by a string of segments connecting the waypoints in pairs. The projection of the three-dimensional trajectory into a horizontal plane is called the lateral trajectory and the projection of the three-dimensional trajectory into a vertical plane is called the vertical trajectory or vertical profile. In practice, the lateral and vertical trajectories are often calculated independently of one another. The lateral trajectory is calculated initially as a function of the list of waypoints of the flight plan. The vertical trajectory is thereafter calculated as a function of the lateral trajectory and of the altitude and speed conditions imposed by the flight plan and by the performance of the aircraft.
During a landing runway approach phase, the determination of the three-dimensional trajectory of the aircraft is subject to additional constraints. Indeed, it is necessary to guarantee that the ground speed of the aircraft at the moment of landing, and more precisely on touchdown of the wheels, is less than or equal to a threshold speed. Likewise, the aircraft must reach the threshold of the landing runway at an altitude that is below a threshold altitude, for example of the order of 50 to 100 feet above the altitude of the runway. Stated otherwise, at the moment at which it crosses the threshold of the landing runway, the aircraft must possess a kinetic energy and potential energy that are below predetermined thresholds. These predetermined thresholds are notably aircraft dependent. With a view to obtaining the required ground speed and the required altitude, a theoretical approach trajectory is calculated by the FMS by starting from the landing runway with a required ground speed and a required altitude (typically an altitude equal to the altitude of the runway threshold +50 feet) and by backtracking either up to a cruising level, for example the last cruising level of the aircraft before the approach and descent phase, or up to the current position of the aircraft. Such calculation is termed “backward” calculation. On the basis of the theoretical approach trajectory, a so-called “real” approach trajectory is calculated by taking account of the performance of the aircraft and of its state, namely notably its altitude, its ground speed, its vertical speed and its mass. The calculation of the real approach trajectory is termed “forward” calculation, insofar as it is carried out on the basis of the current position of the aircraft. A problem with the determination of the theoretical approach trajectory is that it is not necessarily compatible with the aircraft's performance. Stated otherwise, at the moment at which the theoretical approach trajectory is determined, the state of the aircraft, notably its altitude, its ground speed and its mass, may be such that it is physically impossible to put it down with the required ground speed and altitude conditions. Numerically, the “forward” calculation does not succeed in linking up with the “backward” calculation, at the runway.
At the present time, FMSs merely note the discrepancy between the required conditions for landing and the predictions of ground speed and altitude at the moment of landing. It is notably possible to represent visually on a screen the differences in altitude and in speed between the current conditions and the conditions required to cross the runway threshold with the altitude required and the ground speed required for landing. However, this visual information does not make it possible to determine whether or not it is possible to correct the ground speed and the altitude during the final approach so as to reach the runway threshold with the required conditions. Patent application EP 2282173 describes a method for displaying a linkup trajectory toward a final approach trajectory in which an item of information relating to the energy of the aircraft is represented on the approach trajectory. The approach trajectory is for example represented in red when the energy of the aircraft is too high. Thus, the current solutions merely provide an item of information according to which the energy of the aircraft is incompatible with the maximum permissible energy for the landing, and do not propose any lateral or vertical trajectory correction.